Ecology 7th Edition by Manuel Molles

Exercise 6

Suppose you are studying the exchange of organic matter between forests and streams and the landscape you are studying is a mosaic of patches of two forest types: deciduous and coniferous. Part of your study involves determining whether there is a difference in the amount of detritus in streams draining patches of deciduous forest versus those draining coniferous forest. In an initial phase of the study, you take random measurements of the amounts of detritus (g dry weight per m 2 ) in two streams: one draining a deciduous forest patch and one draining a coniferous forest patch:

Your hypothesis is that there is no difference in the amounts of detritus that these two streams contain. However, it turns out that the distribution of detritus within the streams is not normal, and so a sample mean will not accurately reflect the typical amount of detritus per square meter. Also, a t -test is not appropriate for making a statistical comparison of detritus standing stock in the two ecosystems. The alternative is to use a statistical test that does not assume a normal distribution and compares medians not means. One such procedure is the Mann-Whitney test, which uses ranks of measurements or observations made in two populations, rather than the measurements themselves to make a statistical comparison. Here are the same data ordered (ranked) from smallest to largest:
We can now calculate the Mann-Whitney statistic U for the two streams. Let's begin with the stream draining the deciduous forest:

At this point in the Mann-Whitney procedure, the larger of the two U values is compared to a table of critical values (Appendix, table A.2). The applicable critical values are determined by significance level, generally P 0.05, and the sample sizes, n 1 and N₂ , which in this case are n d = 7 and n c = 7. Examining table A.2, we find that the critical value of the Mann-Whitney test statistic for our comparison is 41. Since U d = 43 is greater than 41, we reject the hypothesis that the two streams contain the same standing stock of detritus and accept the alternative hypothesis that the standing stocks of detritus in these two particular streams are different.



Can we conclude from this study that streams draining deciduous versus coniferous forest patches contain different amounts of detritus